The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

ABSTRACT: We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. We compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper–Hofstadter Hamiltonian, and obtain excellent agreement.

Tena Dubček, Karlo Lelas, Dario Jukić, Robert Pezer, Marin Soljačić and Hrvoje Buljan, The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling, New J. Phys. 17, 125002 (2015).